a) Calculate the escape speed on Europa, a satelite of theplanet Jupiter. The ra
ID: 1663008 • Letter: A
Question
a) Calculate the escape speed on Europa, a satelite of theplanet Jupiter. The radius of Europa is 1569 km and the free-fallacceleration at its surface is 1.30 m/s^2. ans: I know Vesp = (2GM/R) however I don't knowwere to gp from there??? b) How high will a particle rise if it leaves the surface ofthe satelite with a vertical velocity of 1.01 km/s? c) With what speed will an object hit the satelite if it isdropped from a height of 1000 km? d) Calculate the mass of Europe. Please help me solve this...I have an idea how to but I'm notsure if I'm right. Thank YOU! a) Calculate the escape speed on Europa, a satelite of theplanet Jupiter. The radius of Europa is 1569 km and the free-fallacceleration at its surface is 1.30 m/s^2. ans: I know Vesp = (2GM/R) however I don't knowwere to gp from there??? b) How high will a particle rise if it leaves the surface ofthe satelite with a vertical velocity of 1.01 km/s? c) With what speed will an object hit the satelite if it isdropped from a height of 1000 km? d) Calculate the mass of Europe. Please help me solve this...I have an idea how to but I'm notsure if I'm right. Thank YOU!Explanation / Answer
Given radius , R = 1569 Km = 1569 * 10 ^ 3 m free-fall acceleration at its surface g = 1.3 m/s^2 (a). Escape velocity v = [ 2GM / R ] we know g = GM / R ^ 2 GM / R = gR So, escape velocity v = [2gR] =[4049400] = 2019.75 m / s (b). From law of conservation of energy ,energy at surface =energy at heighest point P.E atsurface + K.E at surface = P.E at heighst point -GMm / R + ( 1/ 2) m v ' ^ 2 = -GMm / ( R + h) -GM / R + ( 1/ 2) v ' ^ 2 = -GM/ ( R + h) -GM / [( -GM / R) + ( 1/ 2) v ' ^ 2 ]= ( R + h ) where G = Gravitatinal constant = 6.67 * 10 ^ -11 N m ^2 / kg ^ 2 plug the values weget maximum height h value (c). Heigt h ' = 1000 km = 10^ 6 m From law of conservation of energy,energy at surface = energy at heighest point P.E atsurface + K.E at surface = P.E at heighst point -GMm / R + ( 1/ 2) m v ' ^ 2 = -GMm / ( R + h' ) -GM / R + ( 1/ 2) v ' ^ 2 = -GM/ ( R + h') (1/ 2) v ' ^ 2 = [-GM/ ( R + h ')] +[GM/R ] v ' ^ 2 = 2 [-GM/ ( R + h ')] +[GM/R ] v ' = {2 [-GM/ ( R + h ')] +[GM/R ] } plug the values weget required velocity v ' value (d). we know g = GM / R ^ 2 from this mass of Europe M = gR ^ 2 / G plug ther values weget answer P.E atsurface + K.E at surface = P.E at heighst point -GMm / R + ( 1/ 2) m v ' ^ 2 = -GMm / ( R + h' ) -GM / R + ( 1/ 2) v ' ^ 2 = -GM/ ( R + h') (1/ 2) v ' ^ 2 = [-GM/ ( R + h ')] +[GM/R ] v ' ^ 2 = 2 [-GM/ ( R + h ')] +[GM/R ] v ' = {2 [-GM/ ( R + h ')] +[GM/R ] } plug the values weget required velocity v ' value (d). we know g = GM / R ^ 2 from this mass of Europe M = gR ^ 2 / G plug ther values weget answerRelated Questions
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